For bakers, turning a doughnut into a doughnut hole is simple. For a mathematician, it's impossible.

ROBERT SIEGEL, HOST:

From NPR News, this is ALL THINGS CONSIDERED. I'm Robert Siegel.

A program such as ours is timed to the exact second, and occasionally, there are small holes when our mix of news and features doesn't quite fill up our two-hour slot.

So NPR's Joe Palca offered to come to our rescue with some short math and sciencey hole-filling stories, stories about what else - holes.

JOE PALCA, BYLINE: Today, we're going to talk about doughnut holes, those round things you buy in a bakery. To a baker, it's not a troubling question to ask whether you can turn a doughnut into a doughnut hole. Simple. Instead of shaping the dough into a tube and dropping it in the deep fat fryer, you shape the dough into a sphere and drop it in the deep fat fryer.

For a mathematician, the question is more complex. In the mathematical world, a doughnut is referred to as a torus. And mathematicians who study the algebra of shapes have been arguing for more than a century whether there was any way you could bend or twist or compress a doughnut-shaped torus so it would turn into a sphere. In 1904, the French mathematician Henri Poincare said the answer was no, but he couldn't show why with mathematical reasoning, and neither could anyone else until finally 100 years later, the less famous Russian mathematician Grigori Perelman did find a way to prove you can't turn a torus into a doughnut hole.

The moral of the story is if you want a doughnut hole, don't ask a mathematician, ask a baker. But if you want to know about the shape of the universe, the mathematicians who worry about doughnut shapes can probably help with answers.

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